Lateral oscillations of a straight section of a two constant based heterogeneous pipeline
Keywords:heterogeneity, pipe, continuity, base, frequency, elasticity module, density
The study focuses on the natural oscillation of a straight section of an invariably heterogeneous elastic pipeline lying on a twoconstant base devised by P. L. Pasternak. The elasticity module and the specific density are regarded as a continuous function of the pipeline length coordinate, whereas the continuous function is a function that characterizes heterogeneity of the elasticity module together with its first and second derivatives. Hereby, the equation on the motion-relative deflection is a linear equation with variable coefficients of the fourth order. The problem is solved in a combined way: the first stage involves a variables separation method, whereas the second stage is carried out by the Bubnov-Galerkin orthogonality method. Specific values are calculated in the first approximation; the findings are presented in tables and graphs that illustrate dependencies between the circular frequency and heterogeneity-specifying parameters. The calculation results show a significant impact of heterogeneity upon the value of circular frequency and depend on the law of heterogeneity distribution.
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